Exact and heuristic algorithms for the aerial refueling parallel machine scheduling problem with due date-to-deadline window and ready times
► We model the ARSP as a parallel machine scheduling with ready times and time window. ► We formulated a MIP model and develop two heuristics, MATC and SA to minimize TWT. ► Algorithms are tested in terms of solution quality and CPU time. ► MATC is more likely to outperform SA when the problem size...
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Veröffentlicht in: | Computers & industrial engineering 2012-02, Vol.62 (1), p.276-285 |
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description | ► We model the ARSP as a parallel machine scheduling with ready times and time window. ► We formulated a MIP model and develop two heuristics, MATC and SA to minimize TWT. ► Algorithms are tested in terms of solution quality and CPU time. ► MATC is more likely to outperform SA when the problem size increases. ► CPU time performance of MATC is significantly better than SA in both cases.
The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with ready times and due date-to-deadline window to minimize total weighted tardiness. ARSP assumes that the jobs have different ready times and a due date-to-deadline window between refueling due date and a deadline to return without refueling. In this paper, we first formulate the ARSP as a mixed integer programming model. The objective function is a piece-wise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, two heuristics are proposed to obtain solutions in reasonable computation times, namely (1) modified ATC rule (MATC), (2) a simulated annealing method (SA). The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with data randomly generated to represent aerial refueling operations of an in-theater air operation. Solutions provided by both algorithms were compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, MATC is more likely to outperform SA especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of MATC is significantly better than SA in both cases. |
doi_str_mv | 10.1016/j.cie.2011.09.015 |
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The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with ready times and due date-to-deadline window to minimize total weighted tardiness. ARSP assumes that the jobs have different ready times and a due date-to-deadline window between refueling due date and a deadline to return without refueling. In this paper, we first formulate the ARSP as a mixed integer programming model. The objective function is a piece-wise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, two heuristics are proposed to obtain solutions in reasonable computation times, namely (1) modified ATC rule (MATC), (2) a simulated annealing method (SA). The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with data randomly generated to represent aerial refueling operations of an in-theater air operation. Solutions provided by both algorithms were compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, MATC is more likely to outperform SA especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of MATC is significantly better than SA in both cases.</description><identifier>ISSN: 0360-8352</identifier><identifier>EISSN: 1879-0550</identifier><identifier>DOI: 10.1016/j.cie.2011.09.015</identifier><identifier>CODEN: CINDDL</identifier><language>eng</language><publisher>New York: Elsevier Ltd</publisher><subject>Aerial refueling ; Algorithms ; Central processing units ; Computation ; Dispatching rule ; Due date-to-deadline window ; Heuristic ; Heuristic methods ; Integer programming ; Job shops ; Mathematical models ; Military aircraft ; Optimization ; Optimization algorithms ; Parallel machine scheduling ; Production scheduling ; Ready time ; Refueling ; Scheduling ; Simulated annealing ; Studies ; Total weighted tardiness</subject><ispartof>Computers & industrial engineering, 2012-02, Vol.62 (1), p.276-285</ispartof><rights>2011 Elsevier Ltd</rights><rights>Copyright Pergamon Press Inc. Feb 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c357t-a32d3e71014c432c919bf8406821b9bd629e5244b962d14a65fd1c630b98530f3</citedby><cites>FETCH-LOGICAL-c357t-a32d3e71014c432c919bf8406821b9bd629e5244b962d14a65fd1c630b98530f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cie.2011.09.015$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>315,781,785,3551,27929,27930,46000</link.rule.ids></links><search><creatorcontrib>Kaplan, Sezgin</creatorcontrib><creatorcontrib>Rabadi, Ghaith</creatorcontrib><title>Exact and heuristic algorithms for the aerial refueling parallel machine scheduling problem with due date-to-deadline window and ready times</title><title>Computers & industrial engineering</title><description>► We model the ARSP as a parallel machine scheduling with ready times and time window. ► We formulated a MIP model and develop two heuristics, MATC and SA to minimize TWT. ► Algorithms are tested in terms of solution quality and CPU time. ► MATC is more likely to outperform SA when the problem size increases. ► CPU time performance of MATC is significantly better than SA in both cases.
The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with ready times and due date-to-deadline window to minimize total weighted tardiness. ARSP assumes that the jobs have different ready times and a due date-to-deadline window between refueling due date and a deadline to return without refueling. In this paper, we first formulate the ARSP as a mixed integer programming model. The objective function is a piece-wise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, two heuristics are proposed to obtain solutions in reasonable computation times, namely (1) modified ATC rule (MATC), (2) a simulated annealing method (SA). The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with data randomly generated to represent aerial refueling operations of an in-theater air operation. Solutions provided by both algorithms were compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, MATC is more likely to outperform SA especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of MATC is significantly better than SA in both cases.</description><subject>Aerial refueling</subject><subject>Algorithms</subject><subject>Central processing units</subject><subject>Computation</subject><subject>Dispatching rule</subject><subject>Due date-to-deadline window</subject><subject>Heuristic</subject><subject>Heuristic methods</subject><subject>Integer programming</subject><subject>Job shops</subject><subject>Mathematical models</subject><subject>Military aircraft</subject><subject>Optimization</subject><subject>Optimization algorithms</subject><subject>Parallel machine scheduling</subject><subject>Production scheduling</subject><subject>Ready time</subject><subject>Refueling</subject><subject>Scheduling</subject><subject>Simulated annealing</subject><subject>Studies</subject><subject>Total weighted tardiness</subject><issn>0360-8352</issn><issn>1879-0550</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp9kc1u1DAUhS1EJYa2D8DOYsUm4dqOM7ZYoaoFpEpsYG059k3jkZMU22HoO_Sh8TCsWLCydP2dc38OIW8YtAxY__7QuoAtB8Za0C0w-YLsmNrrBqSEl2QHoodGCclfkdc5HwCgk5rtyPPtL-sKtYunE24p5BIctfFhTaFMc6bjmmiZkFpMwUaacNwwhuWBPtpkY8RIZ-umsCDNbkK_nf_SOkSc6bF6UL8h9bZgU9bGo_XxBB_D4tfjn7ap1p5oCTPmK3Ix2pjx-u97Sb7f3X67-dzcf_305ebjfeOE3JfGCu4F7uvenesEd5rpYVQd9IqzQQ--5xol77pB99yzzvZy9Mz1AgatpIBRXJJ3Z9866I8NczFzyA5jtAuuWzbVGdS-oqqib_9BD-uWljqd0aAUcCFkhdgZcmnNud7IPKYw2_RUnU5mvTmYGo85xWNAmxpP1Xw4a7Au-jNgMrkii0MfErpi_Br-o_4NDfaY5g</recordid><startdate>20120201</startdate><enddate>20120201</enddate><creator>Kaplan, Sezgin</creator><creator>Rabadi, Ghaith</creator><general>Elsevier Ltd</general><general>Pergamon Press Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20120201</creationdate><title>Exact and heuristic algorithms for the aerial refueling parallel machine scheduling problem with due date-to-deadline window and ready times</title><author>Kaplan, Sezgin ; Rabadi, Ghaith</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c357t-a32d3e71014c432c919bf8406821b9bd629e5244b962d14a65fd1c630b98530f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Aerial refueling</topic><topic>Algorithms</topic><topic>Central processing units</topic><topic>Computation</topic><topic>Dispatching rule</topic><topic>Due date-to-deadline window</topic><topic>Heuristic</topic><topic>Heuristic methods</topic><topic>Integer programming</topic><topic>Job shops</topic><topic>Mathematical models</topic><topic>Military aircraft</topic><topic>Optimization</topic><topic>Optimization algorithms</topic><topic>Parallel machine scheduling</topic><topic>Production scheduling</topic><topic>Ready time</topic><topic>Refueling</topic><topic>Scheduling</topic><topic>Simulated annealing</topic><topic>Studies</topic><topic>Total weighted tardiness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kaplan, Sezgin</creatorcontrib><creatorcontrib>Rabadi, Ghaith</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computers & industrial engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kaplan, Sezgin</au><au>Rabadi, Ghaith</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact and heuristic algorithms for the aerial refueling parallel machine scheduling problem with due date-to-deadline window and ready times</atitle><jtitle>Computers & industrial engineering</jtitle><date>2012-02-01</date><risdate>2012</risdate><volume>62</volume><issue>1</issue><spage>276</spage><epage>285</epage><pages>276-285</pages><issn>0360-8352</issn><eissn>1879-0550</eissn><coden>CINDDL</coden><abstract>► We model the ARSP as a parallel machine scheduling with ready times and time window. ► We formulated a MIP model and develop two heuristics, MATC and SA to minimize TWT. ► Algorithms are tested in terms of solution quality and CPU time. ► MATC is more likely to outperform SA when the problem size increases. ► CPU time performance of MATC is significantly better than SA in both cases.
The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with ready times and due date-to-deadline window to minimize total weighted tardiness. ARSP assumes that the jobs have different ready times and a due date-to-deadline window between refueling due date and a deadline to return without refueling. In this paper, we first formulate the ARSP as a mixed integer programming model. The objective function is a piece-wise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, two heuristics are proposed to obtain solutions in reasonable computation times, namely (1) modified ATC rule (MATC), (2) a simulated annealing method (SA). The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with data randomly generated to represent aerial refueling operations of an in-theater air operation. Solutions provided by both algorithms were compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, MATC is more likely to outperform SA especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of MATC is significantly better than SA in both cases.</abstract><cop>New York</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.cie.2011.09.015</doi><tpages>10</tpages></addata></record> |
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subjects | Aerial refueling Algorithms Central processing units Computation Dispatching rule Due date-to-deadline window Heuristic Heuristic methods Integer programming Job shops Mathematical models Military aircraft Optimization Optimization algorithms Parallel machine scheduling Production scheduling Ready time Refueling Scheduling Simulated annealing Studies Total weighted tardiness |
title | Exact and heuristic algorithms for the aerial refueling parallel machine scheduling problem with due date-to-deadline window and ready times |
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